Generalizing the Finkelstein-Schoenfeld Test to Incorporate Multiple Alternating Thresholds.

Composite endpoints consisting of both terminal and nonterminal events, such as death and hospitalization, are frequently used in cardiovascular clinical trials. The Finkelstein-Schoenfeld (FS) test provides a way to employ a hierarchical structure to combine fatal and nonfatal events by giving death information an absolute priority, which may limit the contribution of clinically meaningful nonfatal events. To provide a more flexible alternative, we propose the Finkelstein-Schoenfeld with multiple thresholds (FS-MT) test, which extends the standard FS test by incorporating multiple thresholds applied sequentially and alternating across endpoints. A weighted adaptive approach is also developed to help determine the thresholds in FS-MT. The proposed approach retains the statistical properties of the FS test while allowing more flexible use of information from lower priority events. We evaluate the operating characteristics of the proposed test through simulations that vary the follow-up time, the correlation between events, and the treatment effect sizes. A case study based on the Digitalis Investigation Group clinical trial data is presented to further illustrate our proposed method. An R package "FSMT" that implements the proposed methodology has been developed.